Probabilistic Prediction Models for Landslide Hazard Mapping

A joint conditional probability model is proposed to represent a measure of a future landslide hazard, and five estimation procedures for the model are presented. The distribution of past landslides was divided into two groups with respect to a fixed time. A training set consisting of the earlier landslides and the geographical information system-based multi-layer spatial data in the study area was used to construct the prediction maps. The predictions were then cross-validated by comparing them with the remaining later landslides. When the database falls short of providing sufficient support for the prediction, the model allows the introduction of the expert's knowledge to modify the observed frequencies of the landslides with respect to the spatial data. The additional information should improve the prediction results. A case study from the Rio Chincina region in Colombia was used to illustrate the methodologies. Introduction Using spatial data sets based on geographical information systems (GIS) quantitative prediction models have been proposed for landslide hazard mapping (Wang and Unwin, 1992; Carrara et al., 1992; Chung and Fabbri, 1993; van Westen, 1993; Jibson et al., 1998). We propose a unified probabilistic framework for predictive modeling using GIS-based multi-layer spatial data. In the probability models for the prediction of landslide hazard, the hazard at each point or pixel is considered as the joint conditional probability that the pixel will be affected by a future landslide given (conditional to) the information from the spatial input data at the pixel. We present five estimation procedures for the models and also offer a new strategy for visualizing, interpreting, and validating the results of predictions. The five procedures are (1) direct estimation of the joint conditional probability for every pixel based on the past landslides; (2) estimation of the bivariate conditional probabilities for the thematic classes in each layer using the past landslides and then, based on them, computation of the joint conditional probability at each pixel by the Bayesian formula under the conditional independence assumption; (3) estimation as in (2) of the bivariate conditional probabilities for the thematic classes in each layer but under the assumption that the joint conditional probability for every pixel is a linear function of the bivariate conditional probabilities (the linear function is estimated using regression analysis); (4) estimation identical to (2) except that the estimated bivariate conditional probabilities using the past landslides are modified using expert's knowledge before being used to compute the joint conditional probability; and (5) the combination of (3) and (4), again assuming that the joint conditional probability for every pixel is a linear function of the modified bivariate conditional probabilities (here, too, the linear function is estimated using regression analysis). Bayesian formulas for geologic prediction models were used by Spigelhalter (1986) and Agterberg et al. (1990). Chung and Fabbri (1993) have adapted the formulas for geologic hazard zonation as a part of "favorability function" approaches, and the method has been applied to landslide prediction by Chung and Leclerc (1994, Leclerc (1994, Luzi (1995), and Luzi and Fabbri (1995). Multivariate regression analysis for landslide hazard was proposed by Carrara (1983), Carrara et al. (1992), and more recently by Chung et al. (1995). Although some layers of spatial data represent continuous measurements, such as slope angles and distances, as discussed by Chung et al. (1995), a map layer containing continuous measurements is usually converted into a number of classes, i.e., "thematic classification," for producing a new map representing geologic hazard. In general, we may assume that each layer represents a classification map containing a number of thematic classes. A case study from a region in central Colombia, which is affected by rapid debris avalanches, is used to compare these five procedures. Study Area and Test Data Set in the Rio Chincina Area in Central Colombla The catchment of the Rio Chincina, located on the western slope of the central Andean mountain range (Cordillera Central) in Colombia, near the Nevado del Ruiz volcano, was used as a test for various landslide hazard zonation techniques. Van Westen (1993) made an extensive study of the region and constructed the database of the study area. Since then it was made available as an "ideal" case-study data set for many kinds of exercises and experiments on landslide hazard zoning by van Westen et al. (1993), with the name of GISSIZ: training package of Geographic Information Systems on Slope Instability Zonation. It is with that data set that Chung et al. (1995) applied a variety of methods of multivariate regression and reviewed some of those settings as the basis of the analysis. This study broadens the approach to a comparison of other methods in which data-driven approaches and knowledge-driven approaches are considered in isolation and in combination to identify the most successful strategies for hazard prediction. The input data for landslide hazard zonation consist of several layers of map information. Each layer may be the result of map updating by experts, of field verification, and of interpretation of aerial photographs. The prepared maps for the analysis C-J E Chung is with the Geological Survey of Canada, 601 Booth Street, Ottawa, Ontario KIA OE8, Canada. ([email protected]). A. G. Fabbri is with the International Institute of Aerospace Survey and Earth Sciences (ITC), Hengelosestraat 99, P.O. Box 6, 7500 Enschede, The Netherlands, (e-mail: fabbri63itc.d). Photogrammetric Engineering & Remote Sensing Vol. 65, No. 12, December 1999, pp. 1389-1399. 0099-1112/99/6512-1389$3.00/0 O 1999 American Society for Photogrammetry